Provable Guarantees for Sparsity Recovery with Deterministic Missing Data Patterns

Published: 13 Feb 2024, Last Modified: 13 Feb 2024Accepted by TMLREveryoneRevisionsBibTeX
Abstract: We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed dataset is censored by a deterministic, non-uniform filter. Recovering the sparsity pattern in datasets with deterministic missing structure can be arguably more challenging than recovering in a uniformly-at-random scenario. In this paper, we propose an efficient algorithm for missing value imputation by utilizing the topological property of the censorship filter. We then provide novel theoretical results for exact recovery of the sparsity pattern using the proposed imputation strategy. Our analysis shows that, under certain statistical and topological conditions, the hidden sparsity pattern can be recovered consistently with high probability in polynomial time and logarithmic sample complexity.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: We made the final changes requested by the action editor.
Supplementary Material: pdf
Assigned Action Editor: ~Zhihui_Zhu1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1506